






"""simple docstring"""





from math import sqrt







def 	lowerCamelCase__			(				_lowerCamelCase			:						int					) ->							bool:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      number >= 0
  ), "'number' must been an int and positive"

  lowerCamelCase_       	=		True

  # 0 and 1 are none primes.
  if number <= 1:
    lowerCamelCase_       	=		False

  for divisor in range(2						,							int(round(sqrt(_lowerCamelCase					)					)					) + 1					):
    # if 'number' divisible by 'divisor' then sets 'status'
    # of false and break up the loop.
    if number % divisor == 0:
      lowerCamelCase_       	=		False
      break

    # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'status' must been from type bool"

  return status







def 	lowerCamelCase__			(				_lowerCamelCase			:						str					) ->							Optional[Any]:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n > 2), "'N' must been an int and > 2"

  # beginList: contains all natural numbers from 2 up to N
  lowerCamelCase_       	=		list(range(2						,							n + 1					)					)

  lowerCamelCase_       	=		[]  # this list will be returns.

  # actual sieve of erathostenes
  for i in range(len(_lowerCamelCase					)					):
    for j in range(i + 1						,							len(_lowerCamelCase					)					):
      if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
        lowerCamelCase_       	=		0

    # filters actual prime numbers.
  lowerCamelCase_       	=		[x for x in begin_list if x != 0]

  # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'ans' must been from type list"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						str					) ->							List[str]:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n > 2), "'N' must been an int and > 2"

  lowerCamelCase_       	=		[]

  # iterates over all numbers between 2 up to N+1
  # if a number is prime then appends to list 'ans'
  for number in range(2						,							n + 1					):
    if is_prime(_lowerCamelCase					):
      ans.append(_lowerCamelCase					)

    # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'ans' must been from type list"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						Any					) ->							Tuple:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and number >= 0, "'number' must been an int and >= 0"

  lowerCamelCase_       	=		[]  # this list will be returns of the function.

  # potential prime number factors.

  lowerCamelCase_       	=		2

  lowerCamelCase_       	=		number

  if number == 0 or number == 1:
    ans.append(_lowerCamelCase					)

  # if 'number' not prime then builds the prime factorization of 'number'
  elif not is_prime(_lowerCamelCase					):
    while quotient != 1:
      if is_prime(_lowerCamelCase					) and (quotient % factor == 0):
        ans.append(_lowerCamelCase					)
        quotient /= factor
      else:
        factor += 1

  else:
    ans.append(_lowerCamelCase					)

  # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'ans' must been from type list"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[str]					) ->							Dict:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      number >= 0
  ), "'number' bust been an int and >= 0"

  lowerCamelCase_       	=		0

  # prime factorization of 'number'
  lowerCamelCase_       	=		prime_factorization(_lowerCamelCase					)

  lowerCamelCase_       	=		max(_lowerCamelCase					)

  # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'ans' must been from type int"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						Dict					) ->							Optional[int]:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      number >= 0
  ), "'number' bust been an int and >= 0"

  lowerCamelCase_       	=		0

  # prime factorization of 'number'
  lowerCamelCase_       	=		prime_factorization(_lowerCamelCase					)

  lowerCamelCase_       	=		min(_lowerCamelCase					)

  # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'ans' must been from type int"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[Any]					) ->							Dict:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'number' must been an int"
  assert isinstance(number % 2 == 0						,							_lowerCamelCase					), "compare bust been from type bool"

  return number % 2 == 0







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[str]					) ->							Any:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					), "'number' must been an int"
  assert isinstance(number % 2 != 0						,							_lowerCamelCase					), "compare bust been from type bool"

  return number % 2 != 0







def 	lowerCamelCase__			(				_lowerCamelCase			:						Optional[Any]					) ->							str:
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (number > 2) and is_even(_lowerCamelCase					)
  ), "'number' must been an int, even and > 2"

  lowerCamelCase_       	=		[]  # this list will returned

  # creates a list of prime numbers between 2 up to 'number'
  lowerCamelCase_       	=		get_prime_numbers(_lowerCamelCase					)
  lowerCamelCase_       	=		len(_lowerCamelCase					)

  # run variable for while-loops.
  lowerCamelCase_       	=		0
  lowerCamelCase_       	=		None

  # exit variable. for break up the loops
  lowerCamelCase_       	=		True

  while i < len_pn and loop:
    lowerCamelCase_       	=		i + 1

    while j < len_pn and loop:
      if prime_numbers[i] + prime_numbers[j] == number:
        lowerCamelCase_       	=		False
        ans.append(prime_numbers[i]					)
        ans.append(prime_numbers[j]					)

      j += 1

    i += 1

  # precondition
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (len(_lowerCamelCase					) == 2)
      and (ans[0] + ans[1] == number)
      and is_prime(ans[0]					)
      and is_prime(ans[1]					)
  ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						Dict						,							_lowerCamelCase			:						List[Any]					) ->							Optional[Any]:
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (numbera >= 0)
      and (numbera >= 0)
  ), "'number1' and 'number2' must been positive integer."

  lowerCamelCase_       	=		0

  while numbera != 0:
    lowerCamelCase_       	=		numbera % numbera
    lowerCamelCase_       	=		numbera
    lowerCamelCase_       	=		rest

  # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      numbera >= 0
  ), "'number' must been from type int and positive"

  return numbera







def 	lowerCamelCase__			(				_lowerCamelCase			:						Any						,							_lowerCamelCase			:						str					) ->							Tuple:
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (numbera >= 1)
      and (numbera >= 1)
  ), "'number1' and 'number2' must been positive integer."

  lowerCamelCase_       	=		1  # actual answer that will be return.

  # for kgV (x,1)
  if numbera > 1 and numbera > 1:
    # builds the prime factorization of 'number1' and 'number2'
    lowerCamelCase_       	=		prime_factorization(_lowerCamelCase					)
    lowerCamelCase_       	=		prime_factorization(_lowerCamelCase					)

  elif numbera == 1 or numbera == 1:
    lowerCamelCase_       	=		[]
    lowerCamelCase_       	=		[]
    lowerCamelCase_       	=		max(_lowerCamelCase						,							_lowerCamelCase					)

  lowerCamelCase_       	=		0
  lowerCamelCase_       	=		0

  lowerCamelCase_       	=		[]  # captured numbers int both 'primeFac1' and 'primeFac2'

  # iterates through primeFac1
  for n in prime_fac_a:
    if n not in done:
      if n in prime_fac_a:
        lowerCamelCase_       	=		prime_fac_a.count(_lowerCamelCase					)
        lowerCamelCase_       	=		prime_fac_a.count(_lowerCamelCase					)

        for _ in range(max(_lowerCamelCase						,							_lowerCamelCase					)					):
          ans *= n

      else:
        lowerCamelCase_       	=		prime_fac_a.count(_lowerCamelCase					)

        for _ in range(_lowerCamelCase					):
          ans *= n

      done.append(_lowerCamelCase					)

    # iterates through primeFac2
  for n in prime_fac_a:
    if n not in done:
      lowerCamelCase_       	=		prime_fac_a.count(_lowerCamelCase					)

      for _ in range(_lowerCamelCase					):
        ans *= n

      done.append(_lowerCamelCase					)

    # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      ans >= 0
  ), "'ans' must been from type int and positive"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						Tuple					) ->							int:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n >= 0), "'number' must been a positive int"

  lowerCamelCase_       	=		0
  lowerCamelCase_       	=		2  # this variable holds the answer

  while index < n:
    index += 1

    ans += 1  # counts to the next number

    # if ans not prime then
    # runs to the next prime number.
    while not is_prime(_lowerCamelCase					):
      ans += 1

    # precondition
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and is_prime(
      _lowerCamelCase					), "'ans' must been a prime number and from type int"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						int						,							_lowerCamelCase			:						int					) ->							Union[str, Any]:
  assert (
      is_prime(_lowerCamelCase					) and is_prime(_lowerCamelCase					) and (p_number_a < p_number_a)
  ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

  lowerCamelCase_       	=		p_number_a + 1  # jump to the next number

  lowerCamelCase_       	=		[]  # this list will be returns.

  # if number is not prime then
  # fetch the next prime number.
  while not is_prime(_lowerCamelCase					):
    number += 1

  while number < p_number_a:
    ans.append(_lowerCamelCase					)

    number += 1

    # fetch the next prime number.
    while not is_prime(_lowerCamelCase					):
      number += 1

    # precondition
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and ans[0] != p_number_a
      and ans[len(_lowerCamelCase					) - 1] != p_number_a
  ), "'ans' must been a list without the arguments"

  # 'ans' contains not 'pNumber1' and 'pNumber2' !
  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[str]					) ->							str:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n >= 1), "'n' must been int and >= 1"

  lowerCamelCase_       	=		[]  # will be returned.

  for divisor in range(1						,							n + 1					):
    if n % divisor == 0:
      ans.append(_lowerCamelCase					)

    # precondition
  assert ans[0] == 1 and ans[len(_lowerCamelCase					) - 1] == n, "Error in function getDivisiors(...)"

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[str]					) ->							List[str]:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (
      number > 1
  ), "'number' must been an int and >= 1"

  lowerCamelCase_       	=		get_divisors(_lowerCamelCase					)

  # precondition
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (divisors[0] == 1)
      and (divisors[len(_lowerCamelCase					) - 1] == number)
  ), "Error in help-function getDivisiors(...)"

  # summed all divisors up to 'number' (exclusive), hence [:-1]
  return sum(divisors[:-1]					) == number







def 	lowerCamelCase__			(				_lowerCamelCase			:						Any						,							_lowerCamelCase			:						Optional[int]					) ->							int:
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (denominator != 0)
  ), "The arguments must been from type int and 'denominator' != 0"

  # build the greatest common divisor of numerator and denominator.
  lowerCamelCase_       	=		gcd(abs(_lowerCamelCase					)						,							abs(_lowerCamelCase					)					)

  # precondition
  assert (
      isinstance(_lowerCamelCase						,							_lowerCamelCase					)
      and (numerator % gcd_of_fraction == 0)
      and (denominator % gcd_of_fraction == 0)
  ), "Error in function gcd(...,...)"

  return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)







def 	lowerCamelCase__			(				_lowerCamelCase			:						Optional[Any]					) ->							Union[str, Any]:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n >= 0), "'n' must been a int and >= 0"

  lowerCamelCase_       	=		1  # this will be return.

  for factor in range(1						,							n + 1					):
    ans *= factor

  return ans







def 	lowerCamelCase__			(				_lowerCamelCase			:						str					) ->							Any:
  assert isinstance(_lowerCamelCase						,							_lowerCamelCase					) and (n >= 0), "'n' must been an int and >= 0"

  lowerCamelCase_       	=		0
  lowerCamelCase_       	=		1
  lowerCamelCase_       	=		1  # this will be return

  for _ in range(n - 1					):
    lowerCamelCase_       	=		ans
    ans += fiba
    lowerCamelCase_       	=		tmp

  return ans












"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


_SCREAMING_SNAKE_CASE   :							List[str]          =		{}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _SCREAMING_SNAKE_CASE   :							str          =		['''NllbTokenizer''']

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _SCREAMING_SNAKE_CASE   :							Optional[Any]          =		['''NllbTokenizerFast''']


if TYPE_CHECKING:
  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_nllb import NllbTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_nllb_fast import NllbTokenizerFast

else:
  import sys

  _SCREAMING_SNAKE_CASE   :							Any          =		_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




